Optimal Current Waveforms for Brushless Permanent Magnet Motors

In this paper we give energy-optimal excitation current waveforms
for a permanent magnet synchronous motor
that result in a desired average torque.
Our formulation generalizes previous work by including
a general back-EMF waveform,
voltage and current limits,
an arbitrary phase winding connection,
a simple eddy current loss model,
and a trade-off between power loss and torque ripple.
Determining the optimal current waveforms requires solving
a small convex optimization problem.
We give a fast algorithm to find the optimal current
waveforms in around s;
changes in required torque can be handled in around s
even on low-cost processors.
We show that for an ideal motor with sinusoidal back-EMF,
the optimal current waveforms
increase efficiency by several percent in the constant power region.
We also show that, for our model parameters,
a sinusoidal back-EMF gives no performance benefit
over a trapezoidal back-EMF, even in the constant power region,
provided the optimal current waveforms are used.
Another advantage of on-line optimization is the ability to adapt
in real time to changes in the model or requirements, such as
changes in resistance as winding temperature varies, or even gross
changes like the failure of one winding.